MATHEMATICAL INSTITUTIONS II

Course objectives

The main purpose of the course is to give the student a good knowledge of the basic theory of Differential and Integral Calculus of Functions of several variables, as well as of Linear Algebra. Specific objectives : Knowledge and understanding: at the end of the course the student will have learned the basic theory to study functions of several variables both with scalar or vector values. Moreover he/she will be able to study simple linear maps between vector spaces. Applications : at the end of the course the student will be able to solve simple problems which require the use of the differential and integral calculus . In particular he /she will be able to find extremals of functions of several variables and also determine the potential of a vector field. Moreover he/she will have the ability to solve linear systems. Critical abilities: the student will have the basic knowledge to understand the mathematical tools necessary to study Chemistry and Physics and the way to derive some formulas used in these fields. Communication skills: the student will have the ability to expose the topics studied in written and in oral form. Learning skills: the course will improve the logical abilities and of learning of various scientific disciplines.

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CORRADO MASCIA Lecturers' profile
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CORRADO MASCIA Lecturers' profile
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ANDREA DAVINI Lecturers' profile
FRANCESCA DE MARCHIS Lecturers' profile

Program - Frequency - Exams

Course program
Linear Algebra : Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems - Quadratic forms. Functions of several variables : Limit and continuity - Partial and directional derivatives and differentiability- Higher derivatives , Taylor formula - Local and global maxima or minima. Vector valued functions : Regular curves and their length - Integral on curves - Vector fields and their integral on curves - Conservative vector fields. Integral for functions of several variables : Integrals on planar domains, triple integrals- Recduction and change of variables formulas - Gauss Green and Divergence theorems.
Prerequisites
Differential calculus and integrals for functions of one variable
Books
- Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli
Frequency
It is advisable to take the classes
Exam mode
The evaluation is based on a written and oral exam. The last one can be granted depending on the result of the written part. The written exam can be substituted by two intermediate partial exams given after the first half of the course and after the end of the course.
Lesson mode
The classes will be given using a blackboard
Channel 4
FILOMENA PACELLA Lecturers' profile

Program - Frequency - Exams

Course program
Linear Algebra : Vector spaces and linear maps - Matrices - Eigenvalues and eigenvectors - Linear systems - Quadratic forms. Functions of several variables : Limit and continuity - Partial and directional derivatives and differentiability- Higher derivatives , Taylor formula - Local and global maxima or minima. Vector valued functions : Regular curves and their length - Integral on curves - Vector fields and their integral on curves - Conservative vector fields. Integral for functions of several variables : Integrals on planar domains, triple integrals- Recduction and change of variables formulas - Gauss Green and Divergence theorems.
Prerequisites
Differential calculus and integrals for functions of one variable
Books
- Bramanti M., Pagani C.D., Salsa S.: Matematica - Calcolo Infinitesimale e Algebra Lineare - Zanichelli
Teaching mode
The classes of the course will be given in the presence or in hybrid form according to the evolution of the COVID pandemia.
Frequency
It is advisable to take the classes
Exam mode
The evaluation is based on a written and oral exam. The last one can be granted depending on the result of the written part. The written exam can be substituted by two intermediate partial exams given after the first half of the course and after the end of the course.
Bibliography
Marcellini P. - Sbordone C. , Esercitazioni di Matematica II volume - Liguori Editore
Lesson mode
The classes will be given using a blackboard
ANDREA DAVINI Lecturers' profile
  • Lesson code1020340
  • Academic year2025/2026
  • CourseChemical Sciences
  • CurriculumSingle curriculum
  • Year1st year
  • Semester2nd semester
  • SSDMAT/05
  • CFU6
  • Subject areaDiscipline Matematiche, informatiche e fisiche